In what way does the public key encrypted message hash provide a better digital signature than the public-key encrypted message?

A public key encrypted message hash provides a better digital signature because it ensures data integrity and authenticity with greater efficiency. By hashing the message first, only a fixed-size output is encrypted, which is faster and requires less computational power compared to encrypting the entire message. Additionally, the hash uniquely represents the message, allowing for easy verification; if the hash matches upon decryption, it confirms that the message has not been altered. This method is more secure as it reduces the risk of exposing the entire message during encryption.